For the spin-orbit sector, the leading order (LO) effective potential was first computed in [1]}. The next-to-leading order (NLO) potential in [2]}, [3]}, and N\(^2\) LO in [4]}. Partial results for the N\(^3\) LO correction were recently presented in [5]}.
Similarly, for the quadratic in spin sector, the LO effective potential was also computed in [1]}. The NLO in [7]}, [8]}, [9]}, [10]},
N\(^2\) LO in [11]}, [12]}, [13]} and N\(^3\) LO was computed in [14]}, [15]}.
The computation for cubic and higher orders in the spin variables can be found in [16]}, [17]}, [18]}, whereas the finite size effects are described in detail in [10]}, [17]}, [18]}.
The spin-orbit N\(^3\) LO was then completed in [22]} using the techniques of first-order self-force.
